The present invention relates to signal processing technology and more particularly to techniques for enhancing signals, such as by removing noise, artifacts or blur, enhancing sharpness, etc.
It is generally applicable to the enhancement of d-dimensional signals, where d is some positive integer (d≧1). Audio signals are examples of one-dimensional signals. Images are examples of two-dimensional signals. Three-dimensional signals may correspond to, e.g., video sequences or three-dimensional blocks of data such as seismic data or medical imaging data. Enhancement is distinguished from compression which either maintains or degrades the signal in order to construct a compact binary code representing it.
Signal enhancement or restoration is a process that improves an input digital signal by removing noise components or by suppressing existing distortions introduced by some prior transformation or degradation process such as blurring or signal compression process. Sharpening the signal by removing blur is a form of signal restoration as well as removal of compression artifacts or any additive noise.
Many efficient signal enhancement methods are implemented by means of filter banks that transform the signal into a set of subband signals. Wavelet and wavepacket transforms are examples of such subband transformations. Typically, the transformed coefficients are then processed with simple non-linear amplification or attenuation operators such as soft or hard thresholding operators or block thresholding operators, as described in D. Donoho and I. Johnstone “Ideal spatial adaptation via wavelet shrinkage”, Biometrika, vol. 81, pp. 425-455, December 1994 . An inverse subband transform is then used reconstruct an enhanced signal from the processed subband coefficients.
The filter banks used for subband decomposition implement orthogonal or biorthogonal subband transforms with critically-sampled filter banks, as described in M. Vetterli and C. Herley, “Wavelets and filter banks, theory and design”, IEEE Transactions on Signal Processing, vol. 40, no. 9, pp. 2207-2232, September 1992 . The inverse subband transform is performed by means of perfect reconstruction filters. For a signal of size N, the total number of subband coefficients is also equal to N. The memory size and the number of operations required by critically-sampled filter bank transforms is proportional to N. Orthogonal or biorthogonal wavelet transforms are instances of such transforms. These transforms are computationally very efficient but the subsampling incorporated in the filter bank introduces grid artefacts on the reconstruction. This is particularly visible with a Haar wavelet transform where the reconstructed image has block artifacts (see FIG. 14(c)).
Translation-invariant subband transforms have been introduced to avoid such grid artifacts. A translation-invariant subband transform is implemented by means of a filter bank using an “a trou algorithm” without any subsampling, with zeros incorporated between filter coefficients, as described in M. J. Shensa “The discrete wavelet transform: wedding the à trous and Mallat algorithms”, IEEE Transactions on Signal Processing, vol. 40, no. 10, pp. 2464-2482, October 1992 . Translation-invariant subband transforms remove the grid artifacts and generally improve the peak signal-to-noise ratio (PSNR) of enhancement systems compared to equivalent critically-sampled subband transforms. However, they require much larger memory size and computational complexity.
Compared to a critically subsampled filter bank, a translation invariant filter bank increases the memory size and the number of operations by a factor that is approximately equal to the number of frequency subbands. For a wavelet transform computed over J scales, this factor is J+1 for one-dimensional signals, 3J+1 for two-dimensional signals and 7J+1 for three-dimensional signals. The number of scales J is larger than 3 in many applications. For other wavelet packet subband transforms, these factors are often larger than for a wavelet transform.
There is a need for subband transform schemes that attenuate grid artefacts with a smaller computational and memory cost than translation-invariant subband transforms. This is particularly important for large size signals such as images and videos, for real-time processing applications.